In a bowl, combine the flour, cream of tartar, baking soda, and salt. Set this mixture aside.
In a small bowl, stir together the cinnamon and 3 tablespoons sugar. Set aside.
Using a mixer, cream together the 1 1/2 cups sugar and softened butter until light and fluffy.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract until fully incorporated.
Gradually add the dry ingredients to the wet ingredients and mix until just combined.
Shape dough into 1-inch balls, roll in cinnamon-sugar mixture.
Place dough balls 2 inches apart on ungreased cookie sheet.
Bake at 350°F for 8 to 10 minutes.
Cool on cookie sheet 10 minutes then transfer to wire rack to cool completely.